Multiplying Bayes Factors?

alonzivony · December 2017

Hello,
I recently conducted an experiment and followed it with a replication. Both experiments include 2 within-subject conditions. I conducted a Bayesian dependent sample t-test using JASP on each one of them separately and found the for the first experiment BF10 = 0.505 and for the second experiment BF10 = 0.603. I saw in a recent paper that in order to update the BF after the replication I should just multiply the two BF (which would give me BF10 = 0.505*0.642 = 0.304). At the same article it was mentioned that the same result should be observed if I combine the two data sets to a single data set. When I tried that, I found a BF10 of 1.131. Perhaps I'm missing something very trivial?

Thanks a lot for all your help!
Alon

MSB · December 2017

If you simply calculate the second (replication) BF only on the replication sample, you are using the same priors as used in the original BF, even though these should be updated to the posterior distribution estimated after the first sample.
If I understand correctly, in order to used the updated posterior when calculating the second BF, you need to calculate the BF on all the data (from the original + replication), then dividing by the original BF. Or in this case, BF(r) = 1.131/0.642 = 1.762.

(This would be interpreted as follows: given what we know about the difference between the conditions from experiment 1, the data from experiment 2 is 1.762 times more likely under H1 than under H0.)

EJ · December 2017

MSB is spot on. See also, on my website: Ly, A., Etz, A., Marsman, M., & Wagenmakers, E.-J. (2017). Replication Bayes factors from evidence updating. Manuscript submitted for publication. URL: https://psyarxiv.com/u8m2s/

E.J.

alonzivony · December 2017

Thank you both!

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